I dont like the idea of a core. It should be a team concept.
Having said that I will play along.
I believe you need at least two elite level forwards that each can drive a line solo. Ala Kane and Toews.
For me thats McDavid and Hall. Those are my two must haves up front.
Second tier in order of importance: Leon, RNH, Poo, and Ebs. All guys I like but only Leon is a can't touch "core" guy.
Bottom 6 needs a polarizing figure and thats Hendricks. He is a core player Imo.
By default on defense Sekera is a core piece and deserves to be. Klefbom and Nurse are both core pieces but we are stacked on the left side so a trade of equal value for a righty would be tough but understandable.
Guys that need to be moved this year to improve the team: Schultz and Yak. Niether fits in here and need a change of scenery for all involved.